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arXiv · 1209.6258

Non-normal affine monoids

Lukas Katthän
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Abstract

We give a geometric description of the set of holes in a non-normal affine monoid $Q$. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of $k[Q]$. From this, we see how various properties of $k[Q]$ like local normality and Serre's conditions $(R_1)$ and $(S_2)$ are encoded in the geometry of the holes. A combinatorial upper bound for the depth the monoid algebra $k[Q]$ is obtained and some cases where equality holds are identified. We apply this results to seminormal affine monoids.

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Lukas Katthän. 2012-09-27. Non-normal affine monoids. https://arxiv.org/abs/1209.6258

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